Leaving the foil floating would turn it into a big antenna - radiating/coupling noise throughout the area, to every board... you have to review every wired ground connection and make sure they're typically made back to a common point at the power supply (star topology) so they don't pick up each others noisy currents.
There is that 'june production fix' I've seen on Old Crows's...
As far as keeping that midi interface:
a) it's messy, and a hazard to deal with
b) it's power hungry and loading the supply meant only to power the original circuitry - could lead easily to premature failure due to additional load/heating stress (something the folks at KIWI mention as a reason to replace with their modern upgrade - though incredibly expensive!)
c) it covers up and blocks access to way too much circuitry...
d) a new assembly from CHD would keep thing compact and minimize any related headaches of wires / grounds and all the rest
e) A new interface would increase the value of your synth - no if's, ands or buts.....
No doubt there's still work to be done to get rid of those 'gremlin' noises...again, you seriously have to clean things up first before you can deal with that in a reasonably effective manner... just common sense really.
That jumpering was poorly done... also if there's even the slightest bit of battery residue on the board (in the wrong place), it's highly conductive and will connect signals that should otherwise be isolated - the exact symptom I dealt with to fix a fellow's P6.
You can't clean what you can't get at, buried under a mass of poorly installed jumper wires or being blocked by an oversized, oldschool sized interface from the previous century....
These points are rather straight forward, but if you have any doubts about doing it properly, hire a tech or even an assembler... well worth the investment and again increases the serious value of the synth for when you decide to part ways.
Otherwise, poking around forever and a day, however 'entertainingly productive' it may seem and you might still get lucky and find the issue, otherwise just drags out the inevitable....